Vinegar has been around as you can read by these facts i have found on the web for you. There is no one person that was given the acknowledgement of inventing it.

Vinegar residues were found in urns from ancient Egypt and have been traced to 3000 BC.
The first written history of vinegar in China dates to 1200 BC
1000 BC… In ancient Rome different types of vinegar were made from wine, dates, figs and other fruits and placed in bowls for the dunking of bread.
The making of rice vinegar in China goes back 3000 years.
During biblical times, vinegar was used to flavor foods, drunk as an energizing drink, and used as a medicine.
In ancient Greece, around 400 BC, Hippocrates, who is considered the father of modern medicine, prescribed apple cider vinegar mixed with honey for a variety of ailments, including coughs and colds.
Vinegar was used by the Carthaginian general Hannibal when he crossed the Alps with elephants to invade Italy in 218 BC. It was poured over hot boulders to crumble them, to allow his troops to march through.
The Japanese samurai believed drinking a rice vinegar drink would boost their strength and they drank it regularly.
Vinegar throughout history has been useful to everyday soldiers. Diluted vinegar has been used as a strengthening and an energizing tonic by the military throughout the ages. Roman soldiers called this refreshing drink posca. They used it regularly like the Japanese samurai. The addition of vinegar to their drinking water had the additional benefit of killing any infectious agents that might have been present.